#283428 (Java21) No.732 3PrimeCounting

提出ソース

結果

問題	No.732 3PrimeCounting
ユーザー	uwi
提出日時	2018-09-07 21:43:59
言語	Java21 (openjdk 21)
結果	AC
実行時間	902 ms / 3,000 ms
コード長	11,738 bytes
コンパイル時間	4,805 ms
コンパイル使用メモリ	90,052 KB
実行使用メモリ	81,840 KB
最終ジャッジ日時	2024-11-29 12:09:37
合計ジャッジ時間	31,776 ms
ジャッジサーバーID （参考情報）	judge2 / judge4

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	55 ms 37,172 KB
testcase_01	AC	56 ms 37,032 KB
testcase_02	AC	55 ms 37,240 KB
testcase_03	AC	55 ms 37,088 KB
testcase_04	AC	55 ms 37,148 KB
testcase_05	AC	56 ms 37,276 KB
testcase_06	AC	56 ms 37,248 KB
testcase_07	AC	54 ms 37,032 KB
testcase_08	AC	56 ms 37,220 KB
testcase_09	AC	56 ms 36,924 KB
testcase_10	AC	56 ms 37,004 KB
testcase_11	AC	56 ms 37,088 KB
testcase_12	AC	56 ms 37,120 KB
testcase_13	AC	55 ms 37,248 KB
testcase_14	AC	55 ms 37,108 KB
testcase_15	AC	56 ms 37,040 KB
testcase_16	AC	56 ms 37,184 KB
testcase_17	AC	55 ms 37,116 KB
testcase_18	AC	55 ms 36,684 KB
testcase_19	AC	56 ms 37,236 KB
testcase_20	AC	108 ms 40,400 KB
testcase_21	AC	145 ms 43,780 KB
testcase_22	AC	151 ms 44,832 KB
testcase_23	AC	72 ms 38,688 KB
testcase_24	AC	71 ms 38,268 KB
testcase_25	AC	195 ms 44,460 KB
testcase_26	AC	156 ms 44,068 KB
testcase_27	AC	101 ms 39,884 KB
testcase_28	AC	101 ms 40,268 KB
testcase_29	AC	128 ms 41,628 KB
testcase_30	AC	127 ms 41,324 KB
testcase_31	AC	152 ms 44,328 KB
testcase_32	AC	152 ms 44,236 KB
testcase_33	AC	156 ms 44,152 KB
testcase_34	AC	149 ms 44,248 KB
testcase_35	AC	158 ms 44,076 KB
testcase_36	AC	159 ms 44,576 KB
testcase_37	AC	80 ms 39,168 KB
testcase_38	AC	81 ms 38,496 KB
testcase_39	AC	157 ms 44,600 KB
testcase_40	AC	153 ms 44,232 KB
testcase_41	AC	160 ms 44,612 KB
testcase_42	AC	147 ms 43,708 KB
testcase_43	AC	156 ms 44,612 KB
testcase_44	AC	151 ms 44,652 KB
testcase_45	AC	121 ms 41,088 KB
testcase_46	AC	122 ms 41,620 KB
testcase_47	AC	117 ms 41,352 KB
testcase_48	AC	205 ms 44,480 KB
testcase_49	AC	202 ms 44,688 KB
testcase_50	AC	150 ms 43,928 KB
testcase_51	AC	154 ms 44,600 KB
testcase_52	AC	102 ms 40,036 KB
testcase_53	AC	271 ms 48,576 KB
testcase_54	AC	564 ms 57,080 KB
testcase_55	AC	544 ms 59,968 KB
testcase_56	AC	556 ms 57,132 KB
testcase_57	AC	348 ms 54,552 KB
testcase_58	AC	348 ms 54,740 KB
testcase_59	AC	279 ms 48,640 KB
testcase_60	AC	346 ms 54,624 KB
testcase_61	AC	350 ms 54,664 KB
testcase_62	AC	546 ms 57,288 KB
testcase_63	AC	561 ms 56,720 KB
testcase_64	AC	384 ms 54,468 KB
testcase_65	AC	379 ms 54,792 KB
testcase_66	AC	72 ms 38,268 KB
testcase_67	AC	80 ms 38,512 KB
testcase_68	AC	565 ms 60,008 KB
testcase_69	AC	506 ms 56,860 KB
testcase_70	AC	521 ms 59,948 KB
testcase_71	AC	550 ms 59,880 KB
testcase_72	AC	543 ms 59,212 KB
testcase_73	AC	895 ms 81,676 KB
testcase_74	AC	902 ms 81,840 KB
testcase_75	AC	209 ms 44,804 KB
testcase_76	AC	538 ms 56,836 KB
testcase_77	AC	378 ms 54,224 KB
testcase_78	AC	863 ms 69,924 KB
testcase_79	AC	542 ms 59,896 KB
testcase_80	AC	880 ms 69,992 KB
testcase_81	AC	544 ms 59,756 KB
testcase_82	AC	107 ms 40,184 KB
testcase_83	AC	353 ms 54,580 KB
testcase_84	AC	377 ms 54,076 KB
testcase_85	AC	535 ms 57,100 KB
testcase_86	AC	876 ms 69,952 KB
testcase_87	AC	890 ms 77,700 KB
testcase_88	AC	853 ms 78,404 KB

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ソースコード

raw source code

package contest180907;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] primes = sieveEratosthenes(3*n);
		long[] a = new long[n+1];
		for(int p : primes)if(p <= n)a[p] = 1;
		long[] a2 = convolute(a, a);
		long[] a3 = convolute(a2, a);
		
		long[] am2 = new long[2*n+1];
		for(int p : primes)if(p <= n)am2[2*p] = 1;
		long[] am3 = convolute(am2, a);
		
		long ret = 0;
		for(int p : primes) {
			ret += a3[p] - am3[p] * 3;
		}
		out.println(ret/6);
	}
	
		public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681};
		public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};
//		public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033};
//		public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5};
		
		public static long[] convoluteSimply(long[] a, long[] b, int P, int g)
		{
			int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
			long[] fa = nttmb(a, m, false, P, g);
			long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
			for(int i = 0;i < m;i++){
				fa[i] = fa[i]*fb[i]%P;
			}
			return nttmb(fa, m, true, P, g);
		}
		
		public static long[] convolute(long[] a, long[] b)
		{
			int USE = 2;
			int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
			long[][] fs = new long[USE][];
			for(int k = 0;k < USE;k++){
				int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
				long[] fa = nttmb(a, m, false, P, g);
				long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
				for(int i = 0;i < m;i++){
					fa[i] = fa[i]*fb[i]%P;
				}
				fs[k] = nttmb(fa, m, true, P, g);
			}
			
			int[] mods = Arrays.copyOf(NTTPrimes, USE);
			long[] gammas = garnerPrepare(mods);
			int[] buf = new int[USE];
			for(int i = 0;i < fs[0].length;i++){
				for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
				long[] res = garnerBatch(buf, mods, gammas);
				long ret = 0;
				for(int j = res.length-1;j >= 0;j--)ret = ret * mods[j] + res[j];
				fs[0][i] = ret;
			}
			return fs[0];
		}
		
		public static long[] convolute(long[] a, long[] b, int USE, int mod)
		{
			int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
			long[][] fs = new long[USE][];
			for(int k = 0;k < USE;k++){
				int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
				long[] fa = nttmb(a, m, false, P, g);
				long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
				for(int i = 0;i < m;i++){
					fa[i] = fa[i]*fb[i]%P;
				}
				fs[k] = nttmb(fa, m, true, P, g);
			}
			
			int[] mods = Arrays.copyOf(NTTPrimes, USE);
			long[] gammas = garnerPrepare(mods);
			int[] buf = new int[USE];
			for(int i = 0;i < fs[0].length;i++){
				for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
				long[] res = garnerBatch(buf, mods, gammas);
				long ret = 0;
				for(int j = res.length-1;j >= 0;j--)ret = (ret * mods[j] + res[j]) % mod;
				fs[0][i] = ret;
			}
			return fs[0];
		}
		
		// static int[] wws = new int[270000]; // outer faster
		
		// Modifed Montgomery + Barrett
		private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g)
		{
			long[] dst = Arrays.copyOf(src, n);
			
			int h = Integer.numberOfTrailingZeros(n);
			long K = Integer.highestOneBit(P)<<1;
			int H = Long.numberOfTrailingZeros(K)*2;
			long M = K*K/P;
			
			int[] wws = new int[1<<h-1];
			long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
			long w = (1L<<32)%P;
			for(int k = 0;k < 1<<h-1;k++){
				wws[k] = (int)w;
				w = modh(w*dw, M, H, P);
			}
			long J = invl(P, 1L<<32);
			for(int i = 0;i < h;i++){
				for(int j = 0;j < 1<<i;j++){
					for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
						long u = (dst[s] - dst[t] + 2*P)*wws[k];
						dst[s] += dst[t];
						if(dst[s] >= 2*P)dst[s] -= 2*P;
//						long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
						long Q = (u<<32)*J>>>32;
						dst[t] = (u>>>32)-(Q*P>>>32)+P;
					}
				}
				if(i < h-1){
					for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2];
				}
			}
			for(int i = 0;i < n;i++){
				if(dst[i] >= P)dst[i] -= P;
			}
			for(int i = 0;i < n;i++){
				int rev = Integer.reverse(i)>>>-h;
				if(i < rev){
					long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
				}
			}
			
			if(inverse){
				long in = invl(n, P);
				for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P);
			}
			
			return dst;
		}
		
		// Modified Shoup + Barrett
		private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g)
		{
			long[] dst = Arrays.copyOf(src, n);
			
			int h = Integer.numberOfTrailingZeros(n);
			long K = Integer.highestOneBit(P)<<1;
			int H = Long.numberOfTrailingZeros(K)*2;
			long M = K*K/P;
			
			long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
			long[] wws = new long[1<<h-1];
			long[] ws = new long[1<<h-1];
			long w = 1;
			for(int k = 0;k < 1<<h-1;k++){
				wws[k] = (w<<32)/P;
				ws[k] = w;
				w = modh(w*dw, M, H, P);
			}
			for(int i = 0;i < h;i++){
				for(int j = 0;j < 1<<i;j++){
					for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
						long ndsts = dst[s] + dst[t];
						if(ndsts >= 2*P)ndsts -= 2*P;
						long T = dst[s] - dst[t] + 2*P;
						long Q = wws[k]*T>>>32;
						dst[s] = ndsts;
						dst[t] = ws[k]*T-Q*P&(1L<<32)-1;
					}
				}
//				dw = dw * dw % P;
				if(i < h-1){
					for(int k = 0;k < 1<<h-i-2;k++){
						wws[k] = wws[k*2];
						ws[k] = ws[k*2];
					}
				}
			}
			for(int i = 0;i < n;i++){
				if(dst[i] >= P)dst[i] -= P;
			}
			for(int i = 0;i < n;i++){
				int rev = Integer.reverse(i)>>>-h;
				if(i < rev){
					long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
				}
			}
			
			if(inverse){
				long in = invl(n, P);
				for(int i = 0;i < n;i++){
					dst[i] = modh(dst[i] * in, M, H, P);
				}
			}
			
			return dst;
		}
		
		static final long mask = (1L<<31)-1;
		
		public static long modh(long a, long M, int h, int mod)
		{
			long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod;
			return r < mod ? r : r-mod;
		}
		
		private static long[] garnerPrepare(int[] m)
		{
			int n = m.length;
			assert n == m.length;
			if(n == 0)return new long[0];
			long[] gamma = new long[n];
			for(int k = 1;k < n;k++){
				long prod = 1;
				for(int i = 0;i < k;i++){
					prod = prod * m[i] % m[k];
				}
				gamma[k] = invl(prod, m[k]);
			}
			return gamma;
		}
		
		private static long[] garnerBatch(int[] u, int[] m, long[] gamma)
		{
			int n = u.length;
			assert n == m.length;
			long[] v = new long[n];
			v[0] = u[0];
			for(int k = 1;k < n;k++){
				long temp = v[k-1];
				for(int j = k-2;j >= 0;j--){
					temp = (temp * m[j] + v[j]) % m[k];
				}
				v[k] = (u[k] - temp) * gamma[k] % m[k];
				if(v[k] < 0)v[k] += m[k];
			}
			return v;
		}
		
		private static long pow(long a, long n, long mod) {
			//		a %= mod;
			long ret = 1;
			int x = 63 - Long.numberOfLeadingZeros(n);
			for (; x >= 0; x--) {
				ret = ret * ret % mod;
				if (n << 63 - x < 0)
					ret = ret * a % mod;
			}
			return ret;
		}
		
		private static long invl(long a, long mod) {
			long b = mod;
			long p = 1, q = 0;
			while (b > 0) {
				long c = a / b;
				long d;
				d = a;
				a = b;
				b = d % b;
				d = p;
				p = q;
				q = d - c * q;
			}
			return p < 0 ? p + mod : p;
		}

	
	public static int[] sieveEratosthenes(int n) {
		if (n <= 32) {
			int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
			for (int i = 0; i < primes.length; i++) {
				if (n < primes[i]) {
					return Arrays.copyOf(primes, i);
				}
			}
			return primes;
		}

		int u = n + 32;
		double lu = Math.log(u);
		int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
		ret[0] = 2;
		int pos = 1;

		int[] isnp = new int[(n + 1) / 32 / 2 + 1];
		int sup = (n + 1) / 32 / 2 + 1;

		int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
		for (int tp : tprimes) {
			ret[pos++] = tp;
			int[] ptn = new int[tp];
			for (int i = (tp - 3) / 2; i < tp << 5; i += tp)
				ptn[i >> 5] |= 1 << (i & 31);
			for (int j = 0; j < sup; j += tp) {
				for (int i = 0; i < tp && i + j < sup; i++) {
					isnp[j + i] |= ptn[i];
				}
			}
		}

		// 3,5,7
		// 2x+3=n
		int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17,
				9, 6, 16, 5, 15, 14 };
		int h = n / 2;
		for (int i = 0; i < sup; i++) {
			for (int j = ~isnp[i]; j != 0; j &= j - 1) {
				int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
				int p = 2 * pp + 3;
				if (p > n)
					break;
				ret[pos++] = p;
				if ((long) p * p > n)
					continue;
				for (int q = (p * p - 3) / 2; q <= h; q += p)
					isnp[q >> 5] |= 1 << q;
			}
		}

		return Arrays.copyOf(ret, pos);
	}

	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
//			@Override
//			public void run() {
//				long s = System.currentTimeMillis();
//				solve();
//				out.flush();
//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//			}
//		};
//		t.start();
//		t.join();
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}
	
	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}
	
	private int ni() { return (int)nl(); }
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}

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結果

テストケース

ソースコード